We consider a chain of \(N+1\)  superconducting islands. Each
island is connected to its nearest neighbors by Josephson
junctions, so the chain has \(N\)  junctions
(Fig. REF ). We assume \(N\gg {1}\) .
When the junctions are in the
superconducting regime, \(E_J\gg {E}_C\) , the oscillations of the
superconducting phase \(\varphi _n\)  on each island are small.
Then, the Josephson current through the \(n\) th junction from
island \(n\)  to \((n+1)\)  can be written as
\(I_{n}=I_{n}^c\sin (\varphi _{n+1}-\varphi _n) \approx I_{n}^c(\varphi _{n+1}-\varphi _n)\)  [1]}.
Here, \(I_{n}^c=\hbar /(2eL_n) = (2e/\hbar )E_{J,n}\)  is the
junction critical current. Thus, the voltage drop across the
junction can be determined by using the Josephson relation:
\(V_{n+1}-V_n = \frac{\hbar }{2e}\left(\frac{d\varphi _{n+1}}{dt} - \frac{d\varphi _n}{dt}\right)= \frac{\hbar }{2eI_{n}^c}\frac{dI_n}{dt}.\) 
